Thesequence of jobs that are based on decision rule First Come First Served (FCFS). Introduction: First Come First Served is the scheduling rule, which helps to arrange the sequence in the order. Here, the first come would be served first.

Question

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Answer 1

Question

Chapter 15, Problem 17P

a)

Summary Introduction

To determine: Thesequence of jobs that are based on decision rule First Come First Served (FCFS).

Introduction: First Come First Served is the scheduling rule, which helps to arrange the sequence in the order. Here, the first come would be served first.

a)

Expert Solution

Answer to Problem 17P

The sequence is A-B-C-D.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using FCFS:

Job	Processing time	Flow time	Due date	Start	End	Lateness
A	6	6	212	205	210	0
B	3	9	209	211	213	4
C	3	12	208	214	216	8
D	8	20	210	217	224	14

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205.

End day of Job A:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 210.

End day of Job A=Start day+(Duration −1)=205+(6−1)=210

End day of Job B:

Start day of Job B is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 213.

End day of Job B=Start day+(Duration −1)=211+(3−1)=213

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 216.

End day of Job C=Start day+(Duration −1)=214+(3−1)=216

End day of Job D:

Start day of Job D is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 224.

End day of Job D=Start day+(Duration −1)=217+(8−1)=224

Lateness of Job A:

End day of Job A is less than its respective due date. Hence, there would be no lateness.

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 4.

Lateness of Job B=End day−Due date=213−209=4

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 8.

Lateness of Job C=End day−Due date=216−208=8

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 14.

Lateness of Job D=End day−Due date=224−210=14

b)

Summary Introduction

To determine: The sequence of jobs based on decision rule Shortest Processing Time (SPT).

Introduction: Shortest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the shortest duration would be served first. Then, the process would go on from the shortest to largest duration.

b)

Expert Solution

Answer to Problem 17P

The sequence is B-C-A-D.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using SPT:

Job	Processing time	Flow time	Due date	Start	End	Lateness
B	3	3	209	205	207	0
C	3	9	208	208	210	2
A	6	15	212	211	216	4
D	8	20	210	217	224	14

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on duration (processing time). Duration should be assembled in the ascending order.

End day of Job B:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 207.

End day of Job B=Start day+(Duration −1)=205+(3−1)=207

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 210.

End day of Job C=Start day+(Duration −1)=208+(3−1)=210

End day of Job A:

Start day of Job A is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 216.

End day of Job A=Start day+(Duration −1)=211+(6−1)=216

End day of Job D:

Start day of Job D is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 224.

End day of Job D=Start day+(Duration −1)=217+(8−1)=224

Lateness of Job B:

End day of Job Bare less than its respective due date. Hence, there would be no lateness.

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 2.

Lateness of Job C=End day−Due date=210−208=2

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 4.

Lateness of Job A=End day−Due date=216−212=4

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 14.

Lateness of Job D=End day−Due date=224−210=14

c)

Summary Introduction

To determine: The sequence of jobs based on decision rule Longest Processing Time (LPT).

Introduction: Largest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the largest duration would be served first. Then, the process would go on from the largest to shortest duration.

c)

Expert Solution

Answer to Problem 17P

The sequence is D-A-C-B.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using LPT:

Job	Processing time	Flow time	Due date	Start	End	Lateness
D	8	8	210	205	212	2
A	6	14	212	213	218	6
C	3	17	208	219	221	13
B	3	20	209	222	224	15

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on duration (processing time). Duration should be assembled in the descending order

End day of Job D:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 212.

End day of Job D=Start day+(Duration −1)=205+(8−1)=212

End day of Job A:

Start day of Job A is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 218.

End day of Job A=Start day+(Duration −1)=213+(6−1)=218

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 221.

End day of Job C=Start day+(Duration −1)=219+(3−1)=221

End day of Job B:

Start day of Job B is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 224.

End day of Job B=Start day+(Duration −1)=222+(3−1)=224

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 2.

Lateness of Job D=End day−Due date=212−210=2

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 6.

Lateness of Job A=End day−Due date=218−212=6

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 13.

Lateness of Job C=End day−Due date=221−208=13

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 15.

Lateness of Job B=End day−Due date=224−209=15

d)

Summary Introduction

To determine: The sequence of jobs based on decision rule Earliest Due Date (EDD).

Introduction: Earliest Due Date is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the earliest due date would be served first. Then, the process would go on from the earliest due date to latest due date.

d)

Expert Solution

Answer to Problem 17P

The sequence is C-B-D-A.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using EDD:

Job	Processing time	Flow time	Due date	Start	End	Lateness
C	3	3	208	205	207	0
B	3	6	209	208	210	1
D	8	14	210	211	218	8
A	6	20	212	219	224	12

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on due date. Due date should be assembled in the ascending order.

End day of Job C:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 207.

End day of Job C=Start day+(Duration −1)=205+(3−1)=207

End day of Job B:

Start day of Job B is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 210.

End day of Job B=Start day+(Duration −1)=208+(3−1)=210

End day of Job D:

Start day of Job D is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 218.

End day of Job D=Start day+(Duration −1)=211+(8−1)=218

End day of Job A:

Start day of Job A is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 224.

End day of Job A=Start day+(Duration −1)=219+(6−1)=224

Lateness of Job C:

End day of Job Care less than its respective due date. Hence, there would be no lateness.

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 1.

Lateness of Job B=End day−Due date=210−209=1

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 8.

Lateness of Job D=End day−Due date=218−210=8

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 12.

Lateness of Job A=End day−Due date=224−212=12

e)

Summary Introduction

To determine: The sequence of jobs based on critical ratio.

Introduction: Critical ratio is kind of scheduling rule that helps to identify that, the task or job is on the correct track. It would help to identify if the task is behind or ahead of the schedule.

e)

Expert Solution

Answer to Problem 17P

The sequence is D-C-A-B.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Calculate the critical ratio:

Job	Due date	Processing time	Critical ratio
A	212	6	1.17
B	209	3	1.33
C	208	3	1
D	210	8	0.63

Calculate the critical ratio of Job A:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.17.

Critical ratio=(Due date−Present date)Remaining days=212−2056=1.17

Calculate the critical ratio of Job B:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.33.

Critical ratio=(Due date−Present date)Remaining days=209−2053=1.33

Calculate the critical ratio of Job C:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.00.

Critical ratio=(Due date−Present date)Remaining days=208−2053=1.00

Calculate the critical ratio of Job D:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 0.63.

Critical ratio=(Due date−Present date)Remaining days=210−2058=0.63

Sequence based on critical ratio:

Job	Critical ratio
D	0.63
C	1
A	1.17
B	1.33

Determine the sequence of the job using EDD:

Job	Processing time	Flow time	Due date	Start	End	Lateness
D	8	8	210	205	212	2
C	3	11	208	213	215	7
A	6	17	212	216	221	9
B	3	20	209	222	224	15

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on due date. Due date should be assembled in the ascending order.

End day of Job D:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 212.

End day of Job D=Start day+(Duration −1)=205+(8−1)=212

End day of Job C:

Start day of Job C is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 215.

End day of Job C=Start day+(Duration −1)=213+(3−1)=215

End day of Job A:

Start day of Job A is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 221.

End day of Job A=Start day+(Duration −1)=216+(6−1)=221

End day of Job B:

Start day of Job B is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 224.

End day of Job B=Start day+(Duration −1)=222+(3−1)=224

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 2.

Lateness of Job D=End day−Due date=212−210=2

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 7.

Lateness of Job C=End day−Due date=215−208=7

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 9.

Lateness of Job A=End day−Due date=221−212=9

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 15.

Lateness of Job B=End day−Due date=224−209=15

Summary:

Scheduling rule	Average lateness	Average flow time	Average number of jobs in system
FCFS	6.5	11.8	2.4
SPT	5	10.25	2.1
LPT	9	14.8	3
EDD	5.25	10.8	2.2
Critical ratio	8.3	14	2.8

First Come First Served (FCFS):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 6.5.

Average tartiness=Total latenessNumber of jobs=264=6.5

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 11.8.

Average flow time=Total flow timeNumber of jobs=474=11.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.4.

Average flow time=Total flow timeTotal duration=4720=2.4

Shortest Processing Time (SPT):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 5.

Average tartiness=Total latenessNumber of jobs=204=5

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 10.25.

Average flow time=Total flow timeNumber of jobs=514=10.25

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.1.

Average flow time=Total flow timeTotal duration=5120=2.1

Largest Processing Time (LPT):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 9.

Average tartiness=Total latenessNumber of jobs=364=9

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 14.8.

Average flow time=Total flow timeNumber of jobs=594=14.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 3.

Average flow time=Total flow timeTotal duration=5920=3

Earliest Due Date (EDD):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 5.25.

Average tartiness=Total latenessNumber of jobs=214=5.25

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 10.8.

Average flow time=Total flow timeNumber of jobs=434=10.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.2.

Average flow time=Total flow timeTotal duration=4320=2.2

Critical ratio:

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 8.3.

Average tartiness=Total latenessNumber of jobs=364=8.3

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 14.

Average flow time=Total flow timeNumber of jobs=564=14

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.8.

Average flow time=Total flow timeTotal duration=5620=4.8

Conclusion

Shortest processing time has the minimum average tardiness, average flow time, and average number of jobs in systems. Hence, SPT is the best decision rule.

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Students have asked these similar questions

Question 1) Scheduling If the following jobs are sequenced according to the FCFS rule Job Processing Time (days) Due Date A 8 12 B 6 15 C 11 17 D 5 10 E 3 8 What is the mean tardiness (in days) for all jobs? What is the mean completion time in days for all jobs? What is the maximum job tardiness (in days)

Question 4: Six jobs waiting at a workstation will be processed in order, starting with the one with the shortest break time. In the table below, the time elapsed since the arrival of the works, the time remaining to the delivery and the processing time are given. According to this, create the work order and fill in the data in the relevant table.(fill in the second table in the photos)a) What is the average delay time with the generated order?b) How many hours is the average flow time?c) How many jobs will be delayed?d) How many jobs will not be delayed?

Question 34 Consider the processing times and priorities for four jobs: Job Processing time (minutes) Weight/Priority (cost per minute) A 10 6 B 2 1 C 50 2 D 16 10 Assume the weighted shortest processing time (WSPT) rule is used. Which job should be processed third? Group of answer choices A B C D

Answer 2

Question

Chapter 15, Problem 17P

a)

Summary Introduction

To determine: Thesequence of jobs that are based on decision rule First Come First Served (FCFS).

Introduction: First Come First Served is the scheduling rule, which helps to arrange the sequence in the order. Here, the first come would be served first.

a)

Expert Solution

Answer to Problem 17P

The sequence is A-B-C-D.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using FCFS:

Job	Processing time	Flow time	Due date	Start	End	Lateness
A	6	6	212	205	210	0
B	3	9	209	211	213	4
C	3	12	208	214	216	8
D	8	20	210	217	224	14

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205.

End day of Job A:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 210.

End day of Job A=Start day+(Duration −1)=205+(6−1)=210

End day of Job B:

Start day of Job B is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 213.

End day of Job B=Start day+(Duration −1)=211+(3−1)=213

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 216.

End day of Job C=Start day+(Duration −1)=214+(3−1)=216

End day of Job D:

Start day of Job D is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 224.

End day of Job D=Start day+(Duration −1)=217+(8−1)=224

Lateness of Job A:

End day of Job A is less than its respective due date. Hence, there would be no lateness.

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 4.

Lateness of Job B=End day−Due date=213−209=4

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 8.

Lateness of Job C=End day−Due date=216−208=8

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 14.

Lateness of Job D=End day−Due date=224−210=14

b)

Summary Introduction

To determine: The sequence of jobs based on decision rule Shortest Processing Time (SPT).

Introduction: Shortest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the shortest duration would be served first. Then, the process would go on from the shortest to largest duration.

b)

Expert Solution

Answer to Problem 17P

The sequence is B-C-A-D.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using SPT:

Job	Processing time	Flow time	Due date	Start	End	Lateness
B	3	3	209	205	207	0
C	3	9	208	208	210	2
A	6	15	212	211	216	4
D	8	20	210	217	224	14

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on duration (processing time). Duration should be assembled in the ascending order.

End day of Job B:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 207.

End day of Job B=Start day+(Duration −1)=205+(3−1)=207

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 210.

End day of Job C=Start day+(Duration −1)=208+(3−1)=210

End day of Job A:

Start day of Job A is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 216.

End day of Job A=Start day+(Duration −1)=211+(6−1)=216

End day of Job D:

Start day of Job D is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 224.

End day of Job D=Start day+(Duration −1)=217+(8−1)=224

Lateness of Job B:

End day of Job Bare less than its respective due date. Hence, there would be no lateness.

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 2.

Lateness of Job C=End day−Due date=210−208=2

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 4.

Lateness of Job A=End day−Due date=216−212=4

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 14.

Lateness of Job D=End day−Due date=224−210=14

c)

Summary Introduction

To determine: The sequence of jobs based on decision rule Longest Processing Time (LPT).

Introduction: Largest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the largest duration would be served first. Then, the process would go on from the largest to shortest duration.

c)

Expert Solution

Answer to Problem 17P

The sequence is D-A-C-B.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using LPT:

Job	Processing time	Flow time	Due date	Start	End	Lateness
D	8	8	210	205	212	2
A	6	14	212	213	218	6
C	3	17	208	219	221	13
B	3	20	209	222	224	15

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on duration (processing time). Duration should be assembled in the descending order

End day of Job D:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 212.

End day of Job D=Start day+(Duration −1)=205+(8−1)=212

End day of Job A:

Start day of Job A is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 218.

End day of Job A=Start day+(Duration −1)=213+(6−1)=218

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 221.

End day of Job C=Start day+(Duration −1)=219+(3−1)=221

End day of Job B:

Start day of Job B is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 224.

End day of Job B=Start day+(Duration −1)=222+(3−1)=224

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 2.

Lateness of Job D=End day−Due date=212−210=2

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 6.

Lateness of Job A=End day−Due date=218−212=6

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 13.

Lateness of Job C=End day−Due date=221−208=13

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 15.

Lateness of Job B=End day−Due date=224−209=15

d)

Summary Introduction

To determine: The sequence of jobs based on decision rule Earliest Due Date (EDD).

Introduction: Earliest Due Date is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the earliest due date would be served first. Then, the process would go on from the earliest due date to latest due date.

d)

Expert Solution

Answer to Problem 17P

The sequence is C-B-D-A.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using EDD:

Job	Processing time	Flow time	Due date	Start	End	Lateness
C	3	3	208	205	207	0
B	3	6	209	208	210	1
D	8	14	210	211	218	8
A	6	20	212	219	224	12

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on due date. Due date should be assembled in the ascending order.

End day of Job C:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 207.

End day of Job C=Start day+(Duration −1)=205+(3−1)=207

End day of Job B:

Start day of Job B is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 210.

End day of Job B=Start day+(Duration −1)=208+(3−1)=210

End day of Job D:

Start day of Job D is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 218.

End day of Job D=Start day+(Duration −1)=211+(8−1)=218

End day of Job A:

Start day of Job A is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 224.

End day of Job A=Start day+(Duration −1)=219+(6−1)=224

Lateness of Job C:

End day of Job Care less than its respective due date. Hence, there would be no lateness.

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 1.

Lateness of Job B=End day−Due date=210−209=1

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 8.

Lateness of Job D=End day−Due date=218−210=8

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 12.

Lateness of Job A=End day−Due date=224−212=12

e)

Summary Introduction

To determine: The sequence of jobs based on critical ratio.

Introduction: Critical ratio is kind of scheduling rule that helps to identify that, the task or job is on the correct track. It would help to identify if the task is behind or ahead of the schedule.

e)

Expert Solution

Answer to Problem 17P

The sequence is D-C-A-B.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Calculate the critical ratio:

Job	Due date	Processing time	Critical ratio
A	212	6	1.17
B	209	3	1.33
C	208	3	1
D	210	8	0.63

Calculate the critical ratio of Job A:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.17.

Critical ratio=(Due date−Present date)Remaining days=212−2056=1.17

Calculate the critical ratio of Job B:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.33.

Critical ratio=(Due date−Present date)Remaining days=209−2053=1.33

Calculate the critical ratio of Job C:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.00.

Critical ratio=(Due date−Present date)Remaining days=208−2053=1.00

Calculate the critical ratio of Job D:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 0.63.

Critical ratio=(Due date−Present date)Remaining days=210−2058=0.63

Sequence based on critical ratio:

Job	Critical ratio
D	0.63
C	1
A	1.17
B	1.33

Determine the sequence of the job using EDD:

Job	Processing time	Flow time	Due date	Start	End	Lateness
D	8	8	210	205	212	2
C	3	11	208	213	215	7
A	6	17	212	216	221	9
B	3	20	209	222	224	15

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on due date. Due date should be assembled in the ascending order.

End day of Job D:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 212.

End day of Job D=Start day+(Duration −1)=205+(8−1)=212

End day of Job C:

Start day of Job C is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 215.

End day of Job C=Start day+(Duration −1)=213+(3−1)=215

End day of Job A:

Start day of Job A is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 221.

End day of Job A=Start day+(Duration −1)=216+(6−1)=221

End day of Job B:

Start day of Job B is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 224.

End day of Job B=Start day+(Duration −1)=222+(3−1)=224

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 2.

Lateness of Job D=End day−Due date=212−210=2

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 7.

Lateness of Job C=End day−Due date=215−208=7

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 9.

Lateness of Job A=End day−Due date=221−212=9

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 15.

Lateness of Job B=End day−Due date=224−209=15

Summary:

Scheduling rule	Average lateness	Average flow time	Average number of jobs in system
FCFS	6.5	11.8	2.4
SPT	5	10.25	2.1
LPT	9	14.8	3
EDD	5.25	10.8	2.2
Critical ratio	8.3	14	2.8

First Come First Served (FCFS):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 6.5.

Average tartiness=Total latenessNumber of jobs=264=6.5

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 11.8.

Average flow time=Total flow timeNumber of jobs=474=11.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.4.

Average flow time=Total flow timeTotal duration=4720=2.4

Shortest Processing Time (SPT):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 5.

Average tartiness=Total latenessNumber of jobs=204=5

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 10.25.

Average flow time=Total flow timeNumber of jobs=514=10.25

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.1.

Average flow time=Total flow timeTotal duration=5120=2.1

Largest Processing Time (LPT):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 9.

Average tartiness=Total latenessNumber of jobs=364=9

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 14.8.

Average flow time=Total flow timeNumber of jobs=594=14.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 3.

Average flow time=Total flow timeTotal duration=5920=3

Earliest Due Date (EDD):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 5.25.

Average tartiness=Total latenessNumber of jobs=214=5.25

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 10.8.

Average flow time=Total flow timeNumber of jobs=434=10.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.2.

Average flow time=Total flow timeTotal duration=4320=2.2

Critical ratio:

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 8.3.

Average tartiness=Total latenessNumber of jobs=364=8.3

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 14.

Average flow time=Total flow timeNumber of jobs=564=14

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.8.

Average flow time=Total flow timeTotal duration=5620=4.8

Conclusion

Shortest processing time has the minimum average tardiness, average flow time, and average number of jobs in systems. Hence, SPT is the best decision rule.

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Answer 3

Question

Chapter 15, Problem 17P

a)

Summary Introduction

To determine: Thesequence of jobs that are based on decision rule First Come First Served (FCFS).

Introduction: First Come First Served is the scheduling rule, which helps to arrange the sequence in the order. Here, the first come would be served first.

a)

Expert Solution

Answer to Problem 17P

The sequence is A-B-C-D.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using FCFS:

Job	Processing time	Flow time	Due date	Start	End	Lateness
A	6	6	212	205	210	0
B	3	9	209	211	213	4
C	3	12	208	214	216	8
D	8	20	210	217	224	14

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205.

End day of Job A:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 210.

End day of Job A=Start day+(Duration −1)=205+(6−1)=210

End day of Job B:

Start day of Job B is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 213.

End day of Job B=Start day+(Duration −1)=211+(3−1)=213

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 216.

End day of Job C=Start day+(Duration −1)=214+(3−1)=216

End day of Job D:

Start day of Job D is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 224.

End day of Job D=Start day+(Duration −1)=217+(8−1)=224

Lateness of Job A:

End day of Job A is less than its respective due date. Hence, there would be no lateness.

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 4.

Lateness of Job B=End day−Due date=213−209=4

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 8.

Lateness of Job C=End day−Due date=216−208=8

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 14.

Lateness of Job D=End day−Due date=224−210=14

b)

Summary Introduction

To determine: The sequence of jobs based on decision rule Shortest Processing Time (SPT).

Introduction: Shortest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the shortest duration would be served first. Then, the process would go on from the shortest to largest duration.

b)

Expert Solution

Answer to Problem 17P

The sequence is B-C-A-D.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using SPT:

Job	Processing time	Flow time	Due date	Start	End	Lateness
B	3	3	209	205	207	0
C	3	9	208	208	210	2
A	6	15	212	211	216	4
D	8	20	210	217	224	14

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on duration (processing time). Duration should be assembled in the ascending order.

End day of Job B:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 207.

End day of Job B=Start day+(Duration −1)=205+(3−1)=207

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 210.

End day of Job C=Start day+(Duration −1)=208+(3−1)=210

End day of Job A:

Start day of Job A is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 216.

End day of Job A=Start day+(Duration −1)=211+(6−1)=216

End day of Job D:

Start day of Job D is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 224.

End day of Job D=Start day+(Duration −1)=217+(8−1)=224

Lateness of Job B:

End day of Job Bare less than its respective due date. Hence, there would be no lateness.

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 2.

Lateness of Job C=End day−Due date=210−208=2

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 4.

Lateness of Job A=End day−Due date=216−212=4

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 14.

Lateness of Job D=End day−Due date=224−210=14

c)

Summary Introduction

To determine: The sequence of jobs based on decision rule Longest Processing Time (LPT).

Introduction: Largest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the largest duration would be served first. Then, the process would go on from the largest to shortest duration.

c)

Expert Solution

Answer to Problem 17P

The sequence is D-A-C-B.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using LPT:

Job	Processing time	Flow time	Due date	Start	End	Lateness
D	8	8	210	205	212	2
A	6	14	212	213	218	6
C	3	17	208	219	221	13
B	3	20	209	222	224	15

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on duration (processing time). Duration should be assembled in the descending order

End day of Job D:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 212.

End day of Job D=Start day+(Duration −1)=205+(8−1)=212

End day of Job A:

Start day of Job A is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 218.

End day of Job A=Start day+(Duration −1)=213+(6−1)=218

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 221.

End day of Job C=Start day+(Duration −1)=219+(3−1)=221

End day of Job B:

Start day of Job B is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 224.

End day of Job B=Start day+(Duration −1)=222+(3−1)=224

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 2.

Lateness of Job D=End day−Due date=212−210=2

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 6.

Lateness of Job A=End day−Due date=218−212=6

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 13.

Lateness of Job C=End day−Due date=221−208=13

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 15.

Lateness of Job B=End day−Due date=224−209=15

d)

Summary Introduction

To determine: The sequence of jobs based on decision rule Earliest Due Date (EDD).

Introduction: Earliest Due Date is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the earliest due date would be served first. Then, the process would go on from the earliest due date to latest due date.

d)

Expert Solution

Answer to Problem 17P

The sequence is C-B-D-A.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using EDD:

Job	Processing time	Flow time	Due date	Start	End	Lateness
C	3	3	208	205	207	0
B	3	6	209	208	210	1
D	8	14	210	211	218	8
A	6	20	212	219	224	12

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on due date. Due date should be assembled in the ascending order.

End day of Job C:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 207.

End day of Job C=Start day+(Duration −1)=205+(3−1)=207

End day of Job B:

Start day of Job B is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 210.

End day of Job B=Start day+(Duration −1)=208+(3−1)=210

End day of Job D:

Start day of Job D is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 218.

End day of Job D=Start day+(Duration −1)=211+(8−1)=218

End day of Job A:

Start day of Job A is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 224.

End day of Job A=Start day+(Duration −1)=219+(6−1)=224

Lateness of Job C:

End day of Job Care less than its respective due date. Hence, there would be no lateness.

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 1.

Lateness of Job B=End day−Due date=210−209=1

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 8.

Lateness of Job D=End day−Due date=218−210=8

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 12.

Lateness of Job A=End day−Due date=224−212=12

e)

Summary Introduction

To determine: The sequence of jobs based on critical ratio.

Introduction: Critical ratio is kind of scheduling rule that helps to identify that, the task or job is on the correct track. It would help to identify if the task is behind or ahead of the schedule.

e)

Expert Solution

Answer to Problem 17P

The sequence is D-C-A-B.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Calculate the critical ratio:

Job	Due date	Processing time	Critical ratio
A	212	6	1.17
B	209	3	1.33
C	208	3	1
D	210	8	0.63

Calculate the critical ratio of Job A:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.17.

Critical ratio=(Due date−Present date)Remaining days=212−2056=1.17

Calculate the critical ratio of Job B:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.33.

Critical ratio=(Due date−Present date)Remaining days=209−2053=1.33

Calculate the critical ratio of Job C:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.00.

Critical ratio=(Due date−Present date)Remaining days=208−2053=1.00

Calculate the critical ratio of Job D:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 0.63.

Critical ratio=(Due date−Present date)Remaining days=210−2058=0.63

Sequence based on critical ratio:

Job	Critical ratio
D	0.63
C	1
A	1.17
B	1.33

Determine the sequence of the job using EDD:

Job	Processing time	Flow time	Due date	Start	End	Lateness
D	8	8	210	205	212	2
C	3	11	208	213	215	7
A	6	17	212	216	221	9
B	3	20	209	222	224	15

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on due date. Due date should be assembled in the ascending order.

End day of Job D:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 212.

End day of Job D=Start day+(Duration −1)=205+(8−1)=212

End day of Job C:

Start day of Job C is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 215.

End day of Job C=Start day+(Duration −1)=213+(3−1)=215

End day of Job A:

Start day of Job A is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 221.

End day of Job A=Start day+(Duration −1)=216+(6−1)=221

End day of Job B:

Start day of Job B is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 224.

End day of Job B=Start day+(Duration −1)=222+(3−1)=224

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 2.

Lateness of Job D=End day−Due date=212−210=2

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 7.

Lateness of Job C=End day−Due date=215−208=7

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 9.

Lateness of Job A=End day−Due date=221−212=9

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 15.

Lateness of Job B=End day−Due date=224−209=15

Summary:

Scheduling rule	Average lateness	Average flow time	Average number of jobs in system
FCFS	6.5	11.8	2.4
SPT	5	10.25	2.1
LPT	9	14.8	3
EDD	5.25	10.8	2.2
Critical ratio	8.3	14	2.8

First Come First Served (FCFS):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 6.5.

Average tartiness=Total latenessNumber of jobs=264=6.5

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 11.8.

Average flow time=Total flow timeNumber of jobs=474=11.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.4.

Average flow time=Total flow timeTotal duration=4720=2.4

Shortest Processing Time (SPT):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 5.

Average tartiness=Total latenessNumber of jobs=204=5

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 10.25.

Average flow time=Total flow timeNumber of jobs=514=10.25

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.1.

Average flow time=Total flow timeTotal duration=5120=2.1

Largest Processing Time (LPT):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 9.

Average tartiness=Total latenessNumber of jobs=364=9

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 14.8.

Average flow time=Total flow timeNumber of jobs=594=14.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 3.

Average flow time=Total flow timeTotal duration=5920=3

Earliest Due Date (EDD):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 5.25.

Average tartiness=Total latenessNumber of jobs=214=5.25

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 10.8.

Average flow time=Total flow timeNumber of jobs=434=10.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.2.

Average flow time=Total flow timeTotal duration=4320=2.2

Critical ratio:

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 8.3.

Average tartiness=Total latenessNumber of jobs=364=8.3

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 14.

Average flow time=Total flow timeNumber of jobs=564=14

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.8.

Average flow time=Total flow timeTotal duration=5620=4.8

Conclusion

Shortest processing time has the minimum average tardiness, average flow time, and average number of jobs in systems. Hence, SPT is the best decision rule.

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Answer 4

Question

Chapter 15, Problem 17P

a)

Summary Introduction

To determine: Thesequence of jobs that are based on decision rule First Come First Served (FCFS).

Introduction: First Come First Served is the scheduling rule, which helps to arrange the sequence in the order. Here, the first come would be served first.

a)

Expert Solution

Answer to Problem 17P

The sequence is A-B-C-D.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using FCFS:

Job	Processing time	Flow time	Due date	Start	End	Lateness
A	6	6	212	205	210	0
B	3	9	209	211	213	4
C	3	12	208	214	216	8
D	8	20	210	217	224	14

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205.

End day of Job A:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 210.

End day of Job A=Start day+(Duration −1)=205+(6−1)=210

End day of Job B:

Start day of Job B is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 213.

End day of Job B=Start day+(Duration −1)=211+(3−1)=213

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 216.

End day of Job C=Start day+(Duration −1)=214+(3−1)=216

End day of Job D:

Start day of Job D is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 224.

End day of Job D=Start day+(Duration −1)=217+(8−1)=224

Lateness of Job A:

End day of Job A is less than its respective due date. Hence, there would be no lateness.

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 4.

Lateness of Job B=End day−Due date=213−209=4

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 8.

Lateness of Job C=End day−Due date=216−208=8

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 14.

Lateness of Job D=End day−Due date=224−210=14

b)

Summary Introduction

To determine: The sequence of jobs based on decision rule Shortest Processing Time (SPT).

Introduction: Shortest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the shortest duration would be served first. Then, the process would go on from the shortest to largest duration.

b)

Expert Solution

Answer to Problem 17P

The sequence is B-C-A-D.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using SPT:

Job	Processing time	Flow time	Due date	Start	End	Lateness
B	3	3	209	205	207	0
C	3	9	208	208	210	2
A	6	15	212	211	216	4
D	8	20	210	217	224	14

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on duration (processing time). Duration should be assembled in the ascending order.

End day of Job B:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 207.

End day of Job B=Start day+(Duration −1)=205+(3−1)=207

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 210.

End day of Job C=Start day+(Duration −1)=208+(3−1)=210

End day of Job A:

Start day of Job A is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 216.

End day of Job A=Start day+(Duration −1)=211+(6−1)=216

End day of Job D:

Start day of Job D is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 224.

End day of Job D=Start day+(Duration −1)=217+(8−1)=224

Lateness of Job B:

End day of Job Bare less than its respective due date. Hence, there would be no lateness.

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 2.

Lateness of Job C=End day−Due date=210−208=2

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 4.

Lateness of Job A=End day−Due date=216−212=4

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 14.

Lateness of Job D=End day−Due date=224−210=14

c)

Summary Introduction

To determine: The sequence of jobs based on decision rule Longest Processing Time (LPT).

Introduction: Largest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the largest duration would be served first. Then, the process would go on from the largest to shortest duration.

c)

Expert Solution

Answer to Problem 17P

The sequence is D-A-C-B.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using LPT:

Job	Processing time	Flow time	Due date	Start	End	Lateness
D	8	8	210	205	212	2
A	6	14	212	213	218	6
C	3	17	208	219	221	13
B	3	20	209	222	224	15

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on duration (processing time). Duration should be assembled in the descending order

End day of Job D:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 212.

End day of Job D=Start day+(Duration −1)=205+(8−1)=212

End day of Job A:

Start day of Job A is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 218.

End day of Job A=Start day+(Duration −1)=213+(6−1)=218

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 221.

End day of Job C=Start day+(Duration −1)=219+(3−1)=221

End day of Job B:

Start day of Job B is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 224.

End day of Job B=Start day+(Duration −1)=222+(3−1)=224

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 2.

Lateness of Job D=End day−Due date=212−210=2

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 6.

Lateness of Job A=End day−Due date=218−212=6

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 13.

Lateness of Job C=End day−Due date=221−208=13

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 15.

Lateness of Job B=End day−Due date=224−209=15

d)

Summary Introduction

To determine: The sequence of jobs based on decision rule Earliest Due Date (EDD).

Introduction: Earliest Due Date is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the earliest due date would be served first. Then, the process would go on from the earliest due date to latest due date.

d)

Expert Solution

Answer to Problem 17P

The sequence is C-B-D-A.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using EDD:

Job	Processing time	Flow time	Due date	Start	End	Lateness
C	3	3	208	205	207	0
B	3	6	209	208	210	1
D	8	14	210	211	218	8
A	6	20	212	219	224	12

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on due date. Due date should be assembled in the ascending order.

End day of Job C:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 207.

End day of Job C=Start day+(Duration −1)=205+(3−1)=207

End day of Job B:

Start day of Job B is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 210.

End day of Job B=Start day+(Duration −1)=208+(3−1)=210

End day of Job D:

Start day of Job D is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 218.

End day of Job D=Start day+(Duration −1)=211+(8−1)=218

End day of Job A:

Start day of Job A is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 224.

End day of Job A=Start day+(Duration −1)=219+(6−1)=224

Lateness of Job C:

End day of Job Care less than its respective due date. Hence, there would be no lateness.

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 1.

Lateness of Job B=End day−Due date=210−209=1

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 8.

Lateness of Job D=End day−Due date=218−210=8

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 12.

Lateness of Job A=End day−Due date=224−212=12

e)

Summary Introduction

To determine: The sequence of jobs based on critical ratio.

Introduction: Critical ratio is kind of scheduling rule that helps to identify that, the task or job is on the correct track. It would help to identify if the task is behind or ahead of the schedule.

e)

Expert Solution

Answer to Problem 17P

The sequence is D-C-A-B.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Calculate the critical ratio:

Job	Due date	Processing time	Critical ratio
A	212	6	1.17
B	209	3	1.33
C	208	3	1
D	210	8	0.63

Calculate the critical ratio of Job A:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.17.

Critical ratio=(Due date−Present date)Remaining days=212−2056=1.17

Calculate the critical ratio of Job B:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.33.

Critical ratio=(Due date−Present date)Remaining days=209−2053=1.33

Calculate the critical ratio of Job C:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.00.

Critical ratio=(Due date−Present date)Remaining days=208−2053=1.00

Calculate the critical ratio of Job D:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 0.63.

Critical ratio=(Due date−Present date)Remaining days=210−2058=0.63

Sequence based on critical ratio:

Job	Critical ratio
D	0.63
C	1
A	1.17
B	1.33

Determine the sequence of the job using EDD:

Job	Processing time	Flow time	Due date	Start	End	Lateness
D	8	8	210	205	212	2
C	3	11	208	213	215	7
A	6	17	212	216	221	9
B	3	20	209	222	224	15

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on due date. Due date should be assembled in the ascending order.

End day of Job D:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 212.

End day of Job D=Start day+(Duration −1)=205+(8−1)=212

End day of Job C:

Start day of Job C is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 215.

End day of Job C=Start day+(Duration −1)=213+(3−1)=215

End day of Job A:

Start day of Job A is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 221.

End day of Job A=Start day+(Duration −1)=216+(6−1)=221

End day of Job B:

Start day of Job B is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 224.

End day of Job B=Start day+(Duration −1)=222+(3−1)=224

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 2.

Lateness of Job D=End day−Due date=212−210=2

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 7.

Lateness of Job C=End day−Due date=215−208=7

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 9.

Lateness of Job A=End day−Due date=221−212=9

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 15.

Lateness of Job B=End day−Due date=224−209=15

Summary:

Scheduling rule	Average lateness	Average flow time	Average number of jobs in system
FCFS	6.5	11.8	2.4
SPT	5	10.25	2.1
LPT	9	14.8	3
EDD	5.25	10.8	2.2
Critical ratio	8.3	14	2.8

First Come First Served (FCFS):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 6.5.

Average tartiness=Total latenessNumber of jobs=264=6.5

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 11.8.

Average flow time=Total flow timeNumber of jobs=474=11.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.4.

Average flow time=Total flow timeTotal duration=4720=2.4

Shortest Processing Time (SPT):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 5.

Average tartiness=Total latenessNumber of jobs=204=5

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 10.25.

Average flow time=Total flow timeNumber of jobs=514=10.25

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.1.

Average flow time=Total flow timeTotal duration=5120=2.1

Largest Processing Time (LPT):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 9.

Average tartiness=Total latenessNumber of jobs=364=9

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 14.8.

Average flow time=Total flow timeNumber of jobs=594=14.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 3.

Average flow time=Total flow timeTotal duration=5920=3

Earliest Due Date (EDD):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 5.25.

Average tartiness=Total latenessNumber of jobs=214=5.25

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 10.8.

Average flow time=Total flow timeNumber of jobs=434=10.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.2.

Average flow time=Total flow timeTotal duration=4320=2.2

Critical ratio:

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 8.3.

Average tartiness=Total latenessNumber of jobs=364=8.3

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 14.

Average flow time=Total flow timeNumber of jobs=564=14

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.8.

Average flow time=Total flow timeTotal duration=5620=4.8

Conclusion

Shortest processing time has the minimum average tardiness, average flow time, and average number of jobs in systems. Hence, SPT is the best decision rule.

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Answer 5

Chapter 15, Problem 17P

a)

Summary Introduction

To determine: Thesequence of jobs that are based on decision rule First Come First Served (FCFS).

Introduction: First Come First Served is the scheduling rule, which helps to arrange the sequence in the order. Here, the first come would be served first.

a)

Expert Solution

Answer to Problem 17P

The sequence is A-B-C-D.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using FCFS:

Job	Processing time	Flow time	Due date	Start	End	Lateness
A	6	6	212	205	210	0
B	3	9	209	211	213	4
C	3	12	208	214	216	8
D	8	20	210	217	224	14

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205.

End day of Job A:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 210.

End day of Job A=Start day+(Duration −1)=205+(6−1)=210

End day of Job B:

Start day of Job B is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 213.

End day of Job B=Start day+(Duration −1)=211+(3−1)=213

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 216.

End day of Job C=Start day+(Duration −1)=214+(3−1)=216

End day of Job D:

Start day of Job D is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 224.

End day of Job D=Start day+(Duration −1)=217+(8−1)=224

Lateness of Job A:

End day of Job A is less than its respective due date. Hence, there would be no lateness.

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 4.

Lateness of Job B=End day−Due date=213−209=4

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 8.

Lateness of Job C=End day−Due date=216−208=8

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 14.

Lateness of Job D=End day−Due date=224−210=14

b)

Summary Introduction

To determine: The sequence of jobs based on decision rule Shortest Processing Time (SPT).

Introduction: Shortest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the shortest duration would be served first. Then, the process would go on from the shortest to largest duration.

b)

Expert Solution

Answer to Problem 17P

The sequence is B-C-A-D.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using SPT:

Job	Processing time	Flow time	Due date	Start	End	Lateness
B	3	3	209	205	207	0
C	3	9	208	208	210	2
A	6	15	212	211	216	4
D	8	20	210	217	224	14

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on duration (processing time). Duration should be assembled in the ascending order.

End day of Job B:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 207.

End day of Job B=Start day+(Duration −1)=205+(3−1)=207

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 210.

End day of Job C=Start day+(Duration −1)=208+(3−1)=210

End day of Job A:

Start day of Job A is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 216.

End day of Job A=Start day+(Duration −1)=211+(6−1)=216

End day of Job D:

Start day of Job D is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 224.

End day of Job D=Start day+(Duration −1)=217+(8−1)=224

Lateness of Job B:

End day of Job Bare less than its respective due date. Hence, there would be no lateness.

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 2.

Lateness of Job C=End day−Due date=210−208=2

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 4.

Lateness of Job A=End day−Due date=216−212=4

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 14.

Lateness of Job D=End day−Due date=224−210=14

c)

Summary Introduction

To determine: The sequence of jobs based on decision rule Longest Processing Time (LPT).

Introduction: Largest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the largest duration would be served first. Then, the process would go on from the largest to shortest duration.

c)

Expert Solution

Answer to Problem 17P

The sequence is D-A-C-B.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using LPT:

Job	Processing time	Flow time	Due date	Start	End	Lateness
D	8	8	210	205	212	2
A	6	14	212	213	218	6
C	3	17	208	219	221	13
B	3	20	209	222	224	15

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on duration (processing time). Duration should be assembled in the descending order

End day of Job D:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 212.

End day of Job D=Start day+(Duration −1)=205+(8−1)=212

End day of Job A:

Start day of Job A is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 218.

End day of Job A=Start day+(Duration −1)=213+(6−1)=218

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 221.

End day of Job C=Start day+(Duration −1)=219+(3−1)=221

End day of Job B:

Start day of Job B is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 224.

End day of Job B=Start day+(Duration −1)=222+(3−1)=224

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 2.

Lateness of Job D=End day−Due date=212−210=2

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 6.

Lateness of Job A=End day−Due date=218−212=6

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 13.

Lateness of Job C=End day−Due date=221−208=13

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 15.

Lateness of Job B=End day−Due date=224−209=15

d)

Summary Introduction

To determine: The sequence of jobs based on decision rule Earliest Due Date (EDD).

Introduction: Earliest Due Date is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the earliest due date would be served first. Then, the process would go on from the earliest due date to latest due date.

d)

Expert Solution

Answer to Problem 17P

The sequence is C-B-D-A.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using EDD:

Job	Processing time	Flow time	Due date	Start	End	Lateness
C	3	3	208	205	207	0
B	3	6	209	208	210	1
D	8	14	210	211	218	8
A	6	20	212	219	224	12

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on due date. Due date should be assembled in the ascending order.

End day of Job C:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 207.

End day of Job C=Start day+(Duration −1)=205+(3−1)=207

End day of Job B:

Start day of Job B is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 210.

End day of Job B=Start day+(Duration −1)=208+(3−1)=210

End day of Job D:

Start day of Job D is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 218.

End day of Job D=Start day+(Duration −1)=211+(8−1)=218

End day of Job A:

Start day of Job A is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 224.

End day of Job A=Start day+(Duration −1)=219+(6−1)=224

Lateness of Job C:

End day of Job Care less than its respective due date. Hence, there would be no lateness.

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 1.

Lateness of Job B=End day−Due date=210−209=1

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 8.

Lateness of Job D=End day−Due date=218−210=8

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 12.

Lateness of Job A=End day−Due date=224−212=12

e)

Summary Introduction

To determine: The sequence of jobs based on critical ratio.

Introduction: Critical ratio is kind of scheduling rule that helps to identify that, the task or job is on the correct track. It would help to identify if the task is behind or ahead of the schedule.

e)

Expert Solution

Answer to Problem 17P

The sequence is D-C-A-B.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Calculate the critical ratio:

Job	Due date	Processing time	Critical ratio
A	212	6	1.17
B	209	3	1.33
C	208	3	1
D	210	8	0.63

Calculate the critical ratio of Job A:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.17.

Critical ratio=(Due date−Present date)Remaining days=212−2056=1.17

Calculate the critical ratio of Job B:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.33.

Critical ratio=(Due date−Present date)Remaining days=209−2053=1.33

Calculate the critical ratio of Job C:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.00.

Critical ratio=(Due date−Present date)Remaining days=208−2053=1.00

Calculate the critical ratio of Job D:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 0.63.

Critical ratio=(Due date−Present date)Remaining days=210−2058=0.63

Sequence based on critical ratio:

Job	Critical ratio
D	0.63
C	1
A	1.17
B	1.33

Determine the sequence of the job using EDD:

Job	Processing time	Flow time	Due date	Start	End	Lateness
D	8	8	210	205	212	2
C	3	11	208	213	215	7
A	6	17	212	216	221	9
B	3	20	209	222	224	15

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on due date. Due date should be assembled in the ascending order.

End day of Job D:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 212.

End day of Job D=Start day+(Duration −1)=205+(8−1)=212

End day of Job C:

Start day of Job C is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 215.

End day of Job C=Start day+(Duration −1)=213+(3−1)=215

End day of Job A:

Start day of Job A is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 221.

End day of Job A=Start day+(Duration −1)=216+(6−1)=221

End day of Job B:

Start day of Job B is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 224.

End day of Job B=Start day+(Duration −1)=222+(3−1)=224

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 2.

Lateness of Job D=End day−Due date=212−210=2

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 7.

Lateness of Job C=End day−Due date=215−208=7

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 9.

Lateness of Job A=End day−Due date=221−212=9

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 15.

Lateness of Job B=End day−Due date=224−209=15

Summary:

Scheduling rule	Average lateness	Average flow time	Average number of jobs in system
FCFS	6.5	11.8	2.4
SPT	5	10.25	2.1
LPT	9	14.8	3
EDD	5.25	10.8	2.2
Critical ratio	8.3	14	2.8

First Come First Served (FCFS):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 6.5.

Average tartiness=Total latenessNumber of jobs=264=6.5

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 11.8.

Average flow time=Total flow timeNumber of jobs=474=11.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.4.

Average flow time=Total flow timeTotal duration=4720=2.4

Shortest Processing Time (SPT):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 5.

Average tartiness=Total latenessNumber of jobs=204=5

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 10.25.

Average flow time=Total flow timeNumber of jobs=514=10.25

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.1.

Average flow time=Total flow timeTotal duration=5120=2.1

Largest Processing Time (LPT):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 9.

Average tartiness=Total latenessNumber of jobs=364=9

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 14.8.

Average flow time=Total flow timeNumber of jobs=594=14.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 3.

Average flow time=Total flow timeTotal duration=5920=3

Earliest Due Date (EDD):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 5.25.

Average tartiness=Total latenessNumber of jobs=214=5.25

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 10.8.

Average flow time=Total flow timeNumber of jobs=434=10.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.2.

Average flow time=Total flow timeTotal duration=4320=2.2

Critical ratio:

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 8.3.

Average tartiness=Total latenessNumber of jobs=364=8.3

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 14.

Average flow time=Total flow timeNumber of jobs=564=14

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.8.

Average flow time=Total flow timeTotal duration=5620=4.8

Conclusion

Shortest processing time has the minimum average tardiness, average flow time, and average number of jobs in systems. Hence, SPT is the best decision rule.

Answer 6

Chapter 15, Problem 17P

a)

Summary Introduction

To determine: Thesequence of jobs that are based on decision rule First Come First Served (FCFS).

Introduction: First Come First Served is the scheduling rule, which helps to arrange the sequence in the order. Here, the first come would be served first.

a)

Expert Solution

Answer to Problem 17P

The sequence is A-B-C-D.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using FCFS:

Job	Processing time	Flow time	Due date	Start	End	Lateness
A	6	6	212	205	210	0
B	3	9	209	211	213	4
C	3	12	208	214	216	8
D	8	20	210	217	224	14

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205.

End day of Job A:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 210.

End day of Job A=Start day+(Duration −1)=205+(6−1)=210

End day of Job B:

Start day of Job B is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 213.

End day of Job B=Start day+(Duration −1)=211+(3−1)=213

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 216.

End day of Job C=Start day+(Duration −1)=214+(3−1)=216

End day of Job D:

Start day of Job D is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 224.

End day of Job D=Start day+(Duration −1)=217+(8−1)=224

Lateness of Job A:

End day of Job A is less than its respective due date. Hence, there would be no lateness.

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 4.

Lateness of Job B=End day−Due date=213−209=4

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 8.

Lateness of Job C=End day−Due date=216−208=8

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 14.

Lateness of Job D=End day−Due date=224−210=14

Answer 7

Chapter 15, Problem 17P

a)

Summary Introduction

To determine: Thesequence of jobs that are based on decision rule First Come First Served (FCFS).

Introduction: First Come First Served is the scheduling rule, which helps to arrange the sequence in the order. Here, the first come would be served first.

Answer 8

a)

Expert Solution

Answer to Problem 17P

The sequence is A-B-C-D.

Answer 9

a)

Expert Solution

Answer 10

a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using FCFS:

Job	Processing time	Flow time	Due date	Start	End	Lateness
A	6	6	212	205	210	0
B	3	9	209	211	213	4
C	3	12	208	214	216	8
D	8	20	210	217	224	14

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205.

End day of Job A:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 210.

End day of Job A=Start day+(Duration −1)=205+(6−1)=210

End day of Job B:

Start day of Job B is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 213.

End day of Job B=Start day+(Duration −1)=211+(3−1)=213

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 216.

End day of Job C=Start day+(Duration −1)=214+(3−1)=216

End day of Job D:

Start day of Job D is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 224.

End day of Job D=Start day+(Duration −1)=217+(8−1)=224

Lateness of Job A:

End day of Job A is less than its respective due date. Hence, there would be no lateness.

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 4.

Lateness of Job B=End day−Due date=213−209=4

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 8.

Lateness of Job C=End day−Due date=216−208=8

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 14.

Lateness of Job D=End day−Due date=224−210=14

Answer 13

b)

Summary Introduction

To determine: The sequence of jobs based on decision rule Shortest Processing Time (SPT).

Introduction: Shortest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the shortest duration would be served first. Then, the process would go on from the shortest to largest duration.

b)

Expert Solution

Answer to Problem 17P

The sequence is B-C-A-D.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using SPT:

Job	Processing time	Flow time	Due date	Start	End	Lateness
B	3	3	209	205	207	0
C	3	9	208	208	210	2
A	6	15	212	211	216	4
D	8	20	210	217	224	14

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on duration (processing time). Duration should be assembled in the ascending order.

End day of Job B:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 207.

End day of Job B=Start day+(Duration −1)=205+(3−1)=207

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 210.

End day of Job C=Start day+(Duration −1)=208+(3−1)=210

End day of Job A:

Start day of Job A is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 216.

End day of Job A=Start day+(Duration −1)=211+(6−1)=216

End day of Job D:

Start day of Job D is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 224.

End day of Job D=Start day+(Duration −1)=217+(8−1)=224

Lateness of Job B:

End day of Job Bare less than its respective due date. Hence, there would be no lateness.

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 2.

Lateness of Job C=End day−Due date=210−208=2

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 4.

Lateness of Job A=End day−Due date=216−212=4

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 14.

Lateness of Job D=End day−Due date=224−210=14

Answer 14

b)

Summary Introduction

To determine: The sequence of jobs based on decision rule Shortest Processing Time (SPT).

Introduction: Shortest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the shortest duration would be served first. Then, the process would go on from the shortest to largest duration.

Answer 15

b)

Expert Solution

Answer to Problem 17P

The sequence is B-C-A-D.

Answer 16

b)

Expert Solution

Answer 17

b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using SPT:

Job	Processing time	Flow time	Due date	Start	End	Lateness
B	3	3	209	205	207	0
C	3	9	208	208	210	2
A	6	15	212	211	216	4
D	8	20	210	217	224	14

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on duration (processing time). Duration should be assembled in the ascending order.

End day of Job B:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 207.

End day of Job B=Start day+(Duration −1)=205+(3−1)=207

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 210.

End day of Job C=Start day+(Duration −1)=208+(3−1)=210

End day of Job A:

Start day of Job A is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 216.

End day of Job A=Start day+(Duration −1)=211+(6−1)=216

End day of Job D:

Start day of Job D is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 224.

End day of Job D=Start day+(Duration −1)=217+(8−1)=224

Lateness of Job B:

End day of Job Bare less than its respective due date. Hence, there would be no lateness.

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 2.

Lateness of Job C=End day−Due date=210−208=2

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 4.

Lateness of Job A=End day−Due date=216−212=4

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 14.

Lateness of Job D=End day−Due date=224−210=14

Answer 20

c)

Summary Introduction

To determine: The sequence of jobs based on decision rule Longest Processing Time (LPT).

Introduction: Largest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the largest duration would be served first. Then, the process would go on from the largest to shortest duration.

c)

Expert Solution

Answer to Problem 17P

The sequence is D-A-C-B.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using LPT:

Job	Processing time	Flow time	Due date	Start	End	Lateness
D	8	8	210	205	212	2
A	6	14	212	213	218	6
C	3	17	208	219	221	13
B	3	20	209	222	224	15

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on duration (processing time). Duration should be assembled in the descending order

End day of Job D:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 212.

End day of Job D=Start day+(Duration −1)=205+(8−1)=212

End day of Job A:

Start day of Job A is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 218.

End day of Job A=Start day+(Duration −1)=213+(6−1)=218

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 221.

End day of Job C=Start day+(Duration −1)=219+(3−1)=221

End day of Job B:

Start day of Job B is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 224.

End day of Job B=Start day+(Duration −1)=222+(3−1)=224

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 2.

Lateness of Job D=End day−Due date=212−210=2

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 6.

Lateness of Job A=End day−Due date=218−212=6

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 13.

Lateness of Job C=End day−Due date=221−208=13

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 15.

Lateness of Job B=End day−Due date=224−209=15

Answer 21

c)

Summary Introduction

To determine: The sequence of jobs based on decision rule Longest Processing Time (LPT).

Introduction: Largest Processing Tine is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the largest duration would be served first. Then, the process would go on from the largest to shortest duration.

Answer 22

c)

Expert Solution

Answer to Problem 17P

The sequence is D-A-C-B.

Answer 23

c)

Expert Solution

Answer 24

c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using LPT:

Job	Processing time	Flow time	Due date	Start	End	Lateness
D	8	8	210	205	212	2
A	6	14	212	213	218	6
C	3	17	208	219	221	13
B	3	20	209	222	224	15

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on duration (processing time). Duration should be assembled in the descending order

End day of Job D:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 212.

End day of Job D=Start day+(Duration −1)=205+(8−1)=212

End day of Job A:

Start day of Job A is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 218.

End day of Job A=Start day+(Duration −1)=213+(6−1)=218

End day of Job C:

Start day of Job C is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 221.

End day of Job C=Start day+(Duration −1)=219+(3−1)=221

End day of Job B:

Start day of Job B is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 224.

End day of Job B=Start day+(Duration −1)=222+(3−1)=224

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 2.

Lateness of Job D=End day−Due date=212−210=2

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 6.

Lateness of Job A=End day−Due date=218−212=6

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 13.

Lateness of Job C=End day−Due date=221−208=13

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 15.

Lateness of Job B=End day−Due date=224−209=15

Answer 27

d)

Summary Introduction

To determine: The sequence of jobs based on decision rule Earliest Due Date (EDD).

Introduction: Earliest Due Date is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the earliest due date would be served first. Then, the process would go on from the earliest due date to latest due date.

d)

Expert Solution

Answer to Problem 17P

The sequence is C-B-D-A.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using EDD:

Job	Processing time	Flow time	Due date	Start	End	Lateness
C	3	3	208	205	207	0
B	3	6	209	208	210	1
D	8	14	210	211	218	8
A	6	20	212	219	224	12

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on due date. Due date should be assembled in the ascending order.

End day of Job C:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 207.

End day of Job C=Start day+(Duration −1)=205+(3−1)=207

End day of Job B:

Start day of Job B is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 210.

End day of Job B=Start day+(Duration −1)=208+(3−1)=210

End day of Job D:

Start day of Job D is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 218.

End day of Job D=Start day+(Duration −1)=211+(8−1)=218

End day of Job A:

Start day of Job A is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 224.

End day of Job A=Start day+(Duration −1)=219+(6−1)=224

Lateness of Job C:

End day of Job Care less than its respective due date. Hence, there would be no lateness.

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 1.

Lateness of Job B=End day−Due date=210−209=1

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 8.

Lateness of Job D=End day−Due date=218−210=8

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 12.

Lateness of Job A=End day−Due date=224−212=12

Answer 28

d)

Summary Introduction

To determine: The sequence of jobs based on decision rule Earliest Due Date (EDD).

Introduction: Earliest Due Date is the scheduling rule, which helps to arrange the sequence in the order. Here, job with the earliest due date would be served first. Then, the process would go on from the earliest due date to latest due date.

Answer 29

d)

Expert Solution

Answer to Problem 17P

The sequence is C-B-D-A.

Answer 30

d)

Expert Solution

Answer 31

d)

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Determine the sequence of the job using EDD:

Job	Processing time	Flow time	Due date	Start	End	Lateness
C	3	3	208	205	207	0
B	3	6	209	208	210	1
D	8	14	210	211	218	8
A	6	20	212	219	224	12

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on due date. Due date should be assembled in the ascending order.

End day of Job C:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 207.

End day of Job C=Start day+(Duration −1)=205+(3−1)=207

End day of Job B:

Start day of Job B is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 210.

End day of Job B=Start day+(Duration −1)=208+(3−1)=210

End day of Job D:

Start day of Job D is the next day of the end day of Job B. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 218.

End day of Job D=Start day+(Duration −1)=211+(8−1)=218

End day of Job A:

Start day of Job A is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 224.

End day of Job A=Start day+(Duration −1)=219+(6−1)=224

Lateness of Job C:

End day of Job Care less than its respective due date. Hence, there would be no lateness.

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 1.

Lateness of Job B=End day−Due date=210−209=1

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 8.

Lateness of Job D=End day−Due date=218−210=8

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 12.

Lateness of Job A=End day−Due date=224−212=12

Answer 34

e)

Summary Introduction

To determine: The sequence of jobs based on critical ratio.

Introduction: Critical ratio is kind of scheduling rule that helps to identify that, the task or job is on the correct track. It would help to identify if the task is behind or ahead of the schedule.

e)

Expert Solution

Answer to Problem 17P

The sequence is D-C-A-B.

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Calculate the critical ratio:

Job	Due date	Processing time	Critical ratio
A	212	6	1.17
B	209	3	1.33
C	208	3	1
D	210	8	0.63

Calculate the critical ratio of Job A:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.17.

Critical ratio=(Due date−Present date)Remaining days=212−2056=1.17

Calculate the critical ratio of Job B:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.33.

Critical ratio=(Due date−Present date)Remaining days=209−2053=1.33

Calculate the critical ratio of Job C:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.00.

Critical ratio=(Due date−Present date)Remaining days=208−2053=1.00

Calculate the critical ratio of Job D:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 0.63.

Critical ratio=(Due date−Present date)Remaining days=210−2058=0.63

Sequence based on critical ratio:

Job	Critical ratio
D	0.63
C	1
A	1.17
B	1.33

Determine the sequence of the job using EDD:

Job	Processing time	Flow time	Due date	Start	End	Lateness
D	8	8	210	205	212	2
C	3	11	208	213	215	7
A	6	17	212	216	221	9
B	3	20	209	222	224	15

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on due date. Due date should be assembled in the ascending order.

End day of Job D:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 212.

End day of Job D=Start day+(Duration −1)=205+(8−1)=212

End day of Job C:

Start day of Job C is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 215.

End day of Job C=Start day+(Duration −1)=213+(3−1)=215

End day of Job A:

Start day of Job A is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 221.

End day of Job A=Start day+(Duration −1)=216+(6−1)=221

End day of Job B:

Start day of Job B is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 224.

End day of Job B=Start day+(Duration −1)=222+(3−1)=224

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 2.

Lateness of Job D=End day−Due date=212−210=2

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 7.

Lateness of Job C=End day−Due date=215−208=7

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 9.

Lateness of Job A=End day−Due date=221−212=9

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 15.

Lateness of Job B=End day−Due date=224−209=15

Summary:

Scheduling rule	Average lateness	Average flow time	Average number of jobs in system
FCFS	6.5	11.8	2.4
SPT	5	10.25	2.1
LPT	9	14.8	3
EDD	5.25	10.8	2.2
Critical ratio	8.3	14	2.8

First Come First Served (FCFS):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 6.5.

Average tartiness=Total latenessNumber of jobs=264=6.5

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 11.8.

Average flow time=Total flow timeNumber of jobs=474=11.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.4.

Average flow time=Total flow timeTotal duration=4720=2.4

Shortest Processing Time (SPT):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 5.

Average tartiness=Total latenessNumber of jobs=204=5

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 10.25.

Average flow time=Total flow timeNumber of jobs=514=10.25

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.1.

Average flow time=Total flow timeTotal duration=5120=2.1

Largest Processing Time (LPT):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 9.

Average tartiness=Total latenessNumber of jobs=364=9

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 14.8.

Average flow time=Total flow timeNumber of jobs=594=14.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 3.

Average flow time=Total flow timeTotal duration=5920=3

Earliest Due Date (EDD):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 5.25.

Average tartiness=Total latenessNumber of jobs=214=5.25

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 10.8.

Average flow time=Total flow timeNumber of jobs=434=10.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.2.

Average flow time=Total flow timeTotal duration=4320=2.2

Critical ratio:

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 8.3.

Average tartiness=Total latenessNumber of jobs=364=8.3

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 14.

Average flow time=Total flow timeNumber of jobs=564=14

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.8.

Average flow time=Total flow timeTotal duration=5620=4.8

Conclusion

Shortest processing time has the minimum average tardiness, average flow time, and average number of jobs in systems. Hence, SPT is the best decision rule.

Answer 35

e)

Summary Introduction

To determine: The sequence of jobs based on critical ratio.

Introduction: Critical ratio is kind of scheduling rule that helps to identify that, the task or job is on the correct track. It would help to identify if the task is behind or ahead of the schedule.

Answer 36

e)

Expert Solution

Answer to Problem 17P

The sequence is D-C-A-B.

Answer 37

e)

Expert Solution

Answer 38

e)

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

Given information:

The following information has been given:

Job	Due date	Duration (days)
A	212	6
B	209	3
C	208	3
D	210	8

All the jobs are arrived on day 205.

Calculate the critical ratio:

Job	Due date	Processing time	Critical ratio
A	212	6	1.17
B	209	3	1.33
C	208	3	1
D	210	8	0.63

Calculate the critical ratio of Job A:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.17.

Critical ratio=(Due date−Present date)Remaining days=212−2056=1.17

Calculate the critical ratio of Job B:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.33.

Critical ratio=(Due date−Present date)Remaining days=209−2053=1.33

Calculate the critical ratio of Job C:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 1.00.

Critical ratio=(Due date−Present date)Remaining days=208−2053=1.00

Calculate the critical ratio of Job D:

It is calculated by dividing the value attained by subtracting the present date from the due date and the remaining days. Hence, the critical ratio is 0.63.

Critical ratio=(Due date−Present date)Remaining days=210−2058=0.63

Sequence based on critical ratio:

Job	Critical ratio
D	0.63
C	1
A	1.17
B	1.33

Determine the sequence of the job using EDD:

Job	Processing time	Flow time	Due date	Start	End	Lateness
D	8	8	210	205	212	2
C	3	11	208	213	215	7
A	6	17	212	216	221	9
B	3	20	209	222	224	15

Working note:

Duration and due date for the jobs has been given. Flow time is the cumulative value of the duration. Jobs arrival rate is given as 205. The job should be arranged based on due date. Due date should be assembled in the ascending order.

End day of Job D:

Jobs arrival rate is given as 205. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job D is 212.

End day of Job D=Start day+(Duration −1)=205+(8−1)=212

End day of Job C:

Start day of Job C is the next day of the end day of Job D. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job C is 215.

End day of Job C=Start day+(Duration −1)=213+(3−1)=215

End day of Job A:

Start day of Job A is the next day of the end day of Job C. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job A is 221.

End day of Job A=Start day+(Duration −1)=216+(6−1)=221

End day of Job B:

Start day of Job B is the next day of the end day of Job A. End day is calculated by adding the start day with the value attained by subtracting 1 from the duration. Hence, the end day of Job B is 224.

End day of Job B=Start day+(Duration −1)=222+(3−1)=224

Lateness of Job D:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job D is 2.

Lateness of Job D=End day−Due date=212−210=2

Lateness of Job C:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job C is 7.

Lateness of Job C=End day−Due date=215−208=7

Lateness of Job A:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job A is 9.

Lateness of Job A=End day−Due date=221−212=9

Lateness of Job B:

It is calculated by subtracting the end day of the job from the due date of the project. Hence, the lateness of Job B is 15.

Lateness of Job B=End day−Due date=224−209=15

Summary:

Scheduling rule	Average lateness	Average flow time	Average number of jobs in system
FCFS	6.5	11.8	2.4
SPT	5	10.25	2.1
LPT	9	14.8	3
EDD	5.25	10.8	2.2
Critical ratio	8.3	14	2.8

First Come First Served (FCFS):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 6.5.

Average tartiness=Total latenessNumber of jobs=264=6.5

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 11.8.

Average flow time=Total flow timeNumber of jobs=474=11.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.4.

Average flow time=Total flow timeTotal duration=4720=2.4

Shortest Processing Time (SPT):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 5.

Average tartiness=Total latenessNumber of jobs=204=5

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 10.25.

Average flow time=Total flow timeNumber of jobs=514=10.25

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.1.

Average flow time=Total flow timeTotal duration=5120=2.1

Largest Processing Time (LPT):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 9.

Average tartiness=Total latenessNumber of jobs=364=9

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 14.8.

Average flow time=Total flow timeNumber of jobs=594=14.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 3.

Average flow time=Total flow timeTotal duration=5920=3

Earliest Due Date (EDD):

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 5.25.

Average tartiness=Total latenessNumber of jobs=214=5.25

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 10.8.

Average flow time=Total flow timeNumber of jobs=434=10.8

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.2.

Average flow time=Total flow timeTotal duration=4320=2.2

Critical ratio:

Average tardiness:

It is calculated by dividing the total lateness with the number of jobs. Hence, the average tardiness is 8.3.

Average tartiness=Total latenessNumber of jobs=364=8.3

Average flow time:

It is calculated by dividing the total flow time with the number of jobs. Hence, the average flow time is 14.

Average flow time=Total flow timeNumber of jobs=564=14

Average number of jobs in the system:

It is calculated by dividing the total flow time with total duration of all the jobs. Hence, the average number of jobs in the system is 2.8.

Average flow time=Total flow timeTotal duration=5620=4.8

Answer 41

Conclusion

Shortest processing time has the minimum average tardiness, average flow time, and average number of jobs in systems. Hence, SPT is the best decision rule.

Answer 42

Ch. 15 - Prob. 1ED Ch. 15 - Prob. 1DQ Ch. 15 - Prob. 2DQ Ch. 15 - Prob. 3DQ Ch. 15 - Prob. 4DQ Ch. 15 - Prob. 5DQ Ch. 15 - Prob. 6DQ Ch. 15 - Prob. 7DQ Ch. 15 - Prob. 8DQ Ch. 15 - Prob. 9DQ

Thesequence of jobs that are based on decision rule First Come First Served (FCFS). Introduction: First Come First Served is the scheduling rule, which helps to arrange the sequence in the order. Here, the first come would be served first.

Solution Summary: The author explains the scheduling rule First Come First Served, which helps to arrange the sequence in the order.

Concept explainers

To determine: Thesequence of jobs that are based on decision rule First Come First Served (FCFS).

Introduction: First Come First Served is the scheduling rule, which helps to arrange the sequence in the order. Here, the first come would be served first.

Answer to Problem 17P

Explanation of Solution

Answer to Problem 17P

Explanation of Solution

Answer to Problem 17P

Explanation of Solution

Answer to Problem 17P

Explanation of Solution

To determine: The sequence of jobs based on critical ratio.

Introduction: Critical ratio is kind of scheduling rule that helps to identify that, the task or job is on the correct track. It would help to identify if the task is behind or ahead of the schedule.

Answer to Problem 17P

Explanation of Solution

Want to see more full solutions like this?

Chapter 15 Solutions

Thesequence of jobs that are based on decision rule First Come First Served (FCFS). Introduction: First Come First Served is the scheduling rule, which helps to arrange the sequence in the order. Here, the first come would be served first.

Solution Summary: The author explains the scheduling rule First Come First Served, which helps to arrange the sequence in the order.

Concept explainers

To determine: Thesequence of jobs that are based on decision rule First Come First Served (FCFS). Introduction: First Come First Served is the scheduling rule, which helps to arrange the sequence in the order. Here, the first come would be served first.

Answer to Problem 17P

Explanation of Solution

Answer to Problem 17P

Explanation of Solution

Answer to Problem 17P

Explanation of Solution

Answer to Problem 17P

Explanation of Solution

To determine: The sequence of jobs based on critical ratio. Introduction: Critical ratio is kind of scheduling rule that helps to identify that, the task or job is on the correct track. It would help to identify if the task is behind or ahead of the schedule.

Answer to Problem 17P

Explanation of Solution

Want to see more full solutions like this?

Chapter 15 Solutions

To determine: Thesequence of jobs that are based on decision rule First Come First Served (FCFS).

Introduction: First Come First Served is the scheduling rule, which helps to arrange the sequence in the order. Here, the first come would be served first.

To determine: The sequence of jobs based on critical ratio.

Introduction: Critical ratio is kind of scheduling rule that helps to identify that, the task or job is on the correct track. It would help to identify if the task is behind or ahead of the schedule.